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Exact Trig Values

List of some exact values of sin, cos and tan.

$${\theta}$$	sin	cos	tan
9	$${\frac{\sqrt{8 + 2 \sqrt{10 - 2 \sqrt{5}}}}{4}}$$	$${\frac{\sqrt{8 + 2 \sqrt{10 + 2 \sqrt{5}}}}{4}}$$	$${\sqrt{5} + 1 - \sqrt{5 + 2 \sqrt{5}}}$$
15	$${\frac{\sqrt{6} - \sqrt{2}}{4}}$$	$${\frac{\sqrt{6} + \sqrt{2}}{4}}$$	$${2 - \sqrt{3}}$$
18	$${\frac{\sqrt{5} - 1}{4}}$$	$${\frac{\sqrt{10+2\sqrt{5}}}{4}}$$	$${\frac{\sqrt{5 - 2 \sqrt{5}}}{\sqrt{5}}}$$
22.5	$${\frac{\sqrt{2-\sqrt{2}}}{2}}$$	$${\frac{\sqrt{2+\sqrt{2}}}{2}}$$	$${\sqrt{2} - 1}$$
27	$${\frac{\sqrt{8 - 2 \sqrt{10 - 2 \sqrt{5}}}}{4}}$$	$${\frac{\sqrt{8 + 2 \sqrt{10 - 2 \sqrt{5}}}}{4}}$$	$${\sqrt{5} - 1 - \sqrt{5 - 2 \sqrt{5}}}$$
30	$${\frac{1}{2}}$$	$${\frac{\sqrt{3}}{2}}$$	$${\frac{\sqrt{3}}{3}}$$
36	$${\frac{\sqrt{10-2\sqrt{5}}}{4}}$$	$${\frac{\sqrt{5} + 1}{4}}$$	$${\sqrt{5 - 2 \sqrt{5}}}$$
45	$${\frac{\sqrt{2}}{2}}$$	$${\frac{\sqrt{2}}{2}}$$	$${1}$$
54	$${\frac{\sqrt{5} + 1}{4}}$$	$${\frac{\sqrt{10-2\sqrt{5}}}{4}}$$	$${\frac{\sqrt{5 + 2 \sqrt{5}}}{\sqrt{5}}}$$
60	$${\frac{\sqrt{3}}{2}}$$	$${\frac{1}{2}}$$	$${\sqrt{3}}$$
63	$${\frac{\sqrt{8 + 2 \sqrt{10 - 2 \sqrt{5}}}}{4}}$$	$${\frac{\sqrt{8 - 2 \sqrt{10 - 2 \sqrt{5}}}}{4}}$$	$${\sqrt{5} - 1 + \sqrt{5 - 2 \sqrt{5}}}$$
72	$${\frac{\sqrt{10+2\sqrt{5}}}{4}}$$	$${\frac{\sqrt{5} - 1}{4}}$$	$${\sqrt{5 + 2 \sqrt{5}}}$$
75	$${\frac{\sqrt{6} + \sqrt{2}}{4}}$$	$${\frac{\sqrt{6} - \sqrt{2}}{4}}$$	$${2 + \sqrt{3}}$$
81	$${\frac{\sqrt{8 + 2 \sqrt{10 + 2 \sqrt{5}}}}{4}}$$	$${\frac{\sqrt{8 + 2 \sqrt{10 - 2 \sqrt{5}}}}{4}}$$	$${\sqrt{5} + 1 + \sqrt{5 + 2 \sqrt{5}}}$$
90	$${1}$$	$${0}$$	$${\infty}$$
105	$${\frac{\sqrt{6} + \sqrt{2}}{4}}$$	$${\frac{-\sqrt{6} + \sqrt{2}}{4}}$$	$${-2 - \sqrt{3}}$$
120	$${\frac{\sqrt{3}}{2}}$$	$${-\frac{1}{2}}$$	$${-\sqrt{3}}$$
135	$${\frac{\sqrt{2}}{2}}$$	$${-\frac{\sqrt{2}}{2}}$$	$${-1}$$
150	$${\frac{1}{2}}$$	$${-\frac{\sqrt{3}}{2}}$$	$${-\frac{\sqrt{3}}{3}}$$
180	$${0}$$	$${-1}$$	$${0}$$
210	$${-\frac{1}{2}}$$	$${-\frac{\sqrt{3}}{2}}$$	$${\frac{\sqrt{3}}{3}}$$
225	$${-\frac{\sqrt{2}}{2}}$$	$${-\frac{\sqrt{2}}{2}}$$	$${1}$$
240	$${-\frac{\sqrt{3}}{2}}$$	$${-\frac{1}{2}}$$	$${\sqrt{3}}$$
270	$${-1}$$	$${0}$$	$${-\infty}$$
300	$${-\frac{\sqrt{3}}{2}}$$	$${\frac{1}{2}}$$	$${-\sqrt{3}}$$
315	$${-\frac{\sqrt{2}}{2}}$$	$${\frac{\sqrt{2}}{2}}$$	$${-1}$$
330	$${-\frac{1}{2}}$$	$${\frac{\sqrt{3}}{2}}$$	$${-\frac{\sqrt{3}}{3}}$$

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